L1 adaptive control flight testing and extension to nonlinear reference systems with unmatched uncertainty

Building upon prior research efforts deploying L1 adaptive control in remotely piloted aerospace applications, this dissertation presents the progression of in-flight evaluation of L1 adaptive control to manned flight testing on Calspan’s variable stability Learjet and to an augmentation of an autonomous trajectory planner on a multirotor aircraft. These efforts ultimately led to the development of a new L1 adaptive controller for a class of control-affine nonlinear reference systems subject to time-varying, state-dependent matched and unmatched uncertainties. The L1 adaptive controller for the Learjet flight tests was designed as stability augmentation system, modifying the pilot's stick-to-surface commands, and was evaluated in a series of flying and handling qualities tests. The results of the Learjet flight tests demonstrated the ability of the L1 adaptive controller to recover desired flying qualities and safe, consistent handling qualities in the presence of off-nominal dynamics, some of which had severe flying qualities deficiencies and aggressive tendencies toward adverse pilot-aircraft interaction, and simulated aircraft failures. A modification of the Learjet control law was implemented, with a nonlinear reference system and estimation of both matched and unmatched uncertainties, for a multirotor aircraft as an augmentation of a geometric trajectory-tracking baseline controller, tracking a reference trajectory generated by a model predictive path integral trajectory planner. Simulation results demonstrated that, with the L1 augmentation, the vehicle was able to navigate a complex environment in the presence of uncertainty and external disturbances. The new L1 adaptive controller provides a theoretical foundation for the L1 augmentation in the multirotor application, and may be applicable to tilt-rotor, tilt-wing, and split-propulsion vertical takeoff and landing aircraft proliferating in the urban air mobility sector. The theory is based on incremental stability for robust trajectory tracking and uses a piecewise-constant adaptive law. It proposes a feedforward compensator (in the form of an embedded linear parameter-varying system), synthesized for the variational dynamics of the system using linear matrix inequality-based robust control methods to minimize the peak-to-peak gain from unmatched uncertainty to the system state. A realization of the feedforward compensator in the ambient space can be directly applied to the nonlinear system. Analysis of the closed-loop system provides an incremental stability guarantee and bounds the transient and steady-state trajectory-tracking error

Two new extensions to L1 adaptive control theory

This thesis introduces two new extensions to L1 adaptive control theory. The first is an L1 adaptive state feedback controller with generalized proportional adaptation law for a class of linear systems with input–gain uncertainties and unmatched nonlinear disturbances. The proportional adaptation law provides an adaptive estimate that is directly proportional to the error between the output of the system and the state predictor. One advantage of the new adaptive law is the additional phase margin in the estimation loop, allowing for accommodation of first order sensor dynamics in the state predictor. An additional benefit is the reduction of the required computational resources, since the error bounds reduce at a rate directly proportional to the adaptation gain as compared to the square root of the adaptation gain achieved by the L1 adaptive controllers using gradient descent adaptation laws. In addition, an L1 adaptive funnel controller and variable dependent adaptation law are provided as particular cases for the generalized proportional framework. Also presented is the connection between the generalized proportional feedback law and previous L1 switching controller. The second extension is an L1 adaptive controller for a class of uncertain systems in the presence of time and output dependent unknown nonlinearities and uncertain input matrix with performance specifications defined via a time–varying reference system using output feedback. It is shown that both extensions exhibit the standard characteristics of the L1 adaptive control theory: scaling of transient responses, a guaranteed time–delay margin at high adaptation rates, and the trade off between robustness and performance is determined by the design of a low pass filter

Fault tolerant control of a quadrotor using L-1 adaptive control

Purpose – The growing use of small unmanned rotorcraft in civilian applications means that safe operation is increasingly important. The purpose of this paper is to investigate the fault tolerant properties to faults in the actuators of an L1 adaptive controller for a quadrotor vehicle. Design/methodology/approach – L1 adaptive control provides fast adaptation along with decoupling between adaptation and robustness. This makes the approach a suitable candidate for fault tolerant control of quadrotor and other multirotor vehicles. In the paper, the design of an L1 adaptive controller is presented. The controller is compared to a fixed-gain LQR controller. Findings – The L1 adaptive controller is shown to have improved performance when subject to actuator faults, and a higher range of actuator fault tolerance. Research limitations/implications – The control scheme is tested in simulation of a simple model that ignores aerodynamic and gyroscopic effects. Hence for further work, testing with a more complete model is recommended followed by implementation on an actual platform and flight test. The effect of sensor noise should also be considered along with investigation into the influence of wind disturbances and tolerance to sensor failures. Furthermore, quadrotors cannot tolerate total failure of a rotor without loss of control of one of the degrees of freedom, this aspect requires further investigation. Practical implications – Applying the L1 adaptive controller to a hexrotor or octorotor would increase the reliability of such vehicles without recourse to methods that require fault detection schemes and control reallocation as well as providing tolerance to a total loss of a rotor. Social implications – In order for quadrotors and other similar unmanned air vehicles to undertake many proposed roles, a high level of safety is required. Hence the controllers should be fault tolerant. Originality/value – Fault tolerance to partial actuator/effector faults is demonstrated using an L1 adaptive controller

Analysis, filtering, and control for Takagi-Sugeno fuzzy models in networked systems

Copyright © 2015 Sunjie Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.The fuzzy logic theory has been proven to be effective in dealing with various nonlinear systems and has a great success in industry applications. Among different kinds of models for fuzzy systems, the so-called Takagi-Sugeno (T-S) fuzzy model has been quite popular due to its convenient and simple dynamic structure as well as its capability of approximating any smooth nonlinear function to any specified accuracy within any compact set. In terms of such a model, the performance analysis and the design of controllers and filters play important roles in the research of fuzzy systems. In this paper, we aim to survey some recent advances on the T-S fuzzy control and filtering problems with various network-induced phenomena. The network-induced phenomena under consideration mainly include communication delays, packet dropouts, signal quantization, and randomly occurring uncertainties (ROUs). With such network-induced phenomena, the developments on T-S fuzzy control and filtering issues are reviewed in detail. In addition, some latest results on this topic are highlighted. In the end, conclusions are drawn and some possible future research directions are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grants 61134009, 61329301, 11301118 and 61174136, the Natural Science Foundation of Jiangsu Province of China under Grant BK20130017, the Fundamental Research Funds for the Central Universities of China under Grant CUSF-DH-D-2013061, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany